Yes and no.
It depends on your definition of square root. By the actual one, yes. All non-negative numbers have a square root. That square root might be irrational but it has a square root, nonetheless. 10 isn't a square number because there's no integer that can be squared to make ten but 10 definitely has a square root: 3.16227766.......
If by square root you mean an integer square root, then no. If a number has an integer as its square root then you could square that integer to get the number, making it a square number.
They are called real numbers. Negative square roots must be complex numbers.
No. The square roots of perfect squares are rational.
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
There are no following numbers!
The square roots of negative numbers.
No. The square roots 8 are irrational, as are the square roots of most even numbers.
Numbers with square roots that are whole numbers
They are called real numbers. Negative square roots must be complex numbers.
No. Lots of square roots are not rational. Only the square roots of perfect square numbers are rational. So for example, the square root of 2 is not rational and the square root of 4 is rational.
No. The square roots of perfect squares are rational.
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
Negative numbers have no real square roots. In terms of complex numbers, the square roots of 43 are +j6.5574 (rounded) and -j6.5574 (rounded)
There are no following numbers!
Square roots of negative numbers ARE possible. I guess you haven't been introduced to "imaginary numbers" and the letter "i".
Rational numbers whose square roots are whole numbers are themselves whole numbers. They are called square numbers, e.g. 1, 4, 9, 16, 25 and so on.
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
A number with a square root is still a number. So the answer is all of them.